In The Awakening, racing is obviously a metaphor (a picture, a comparison) for what's going on with Edna. In many ways racing is exhilarating and dangerous and forbidden--all the things Edna's feeling about her short-lived relationship with Alcée Arobin and her more serious and lasting relationship with Robert, as well as her attempt at becoming an artist.
This novel is set in a time and place which sees women in certain roles. We see Adele as one kind of woman, the loving and doting mother figure. We see Madamoiselle Reisz as another, kind of an eccentric artist. We meet a whole slew of fashionable ladies, such as Mrs. Highcamp, who were a bit "naughty" but only within acceptable boundaries. Edna fits none of these very well, though she dabbles in each of these roles.
She has chosen to live dangerously, to flaunt the role she once had, and it's a risk. It's a gamble she loses, in the end, but she ran her race and took her chances.
the reason the race track is a setting is b/c it symbolizing the risk or gamble that Edna takes. At a race track you take chances and bets, but you don't really know the outcome or end result will be. usually you make a bet based on a gut feeling, people don't always think it through.
That realtes to her relationship with Arobin. She is taking a chance by spending time and flirting and kissing him, but she really doesn't know what that will lead to and how it will effect her life or anyone elses for that matter. She just does it because she wants to and acts on feeling.